Recent advances in energy transfer technology is boosting the development of renewable sensor networks. To sustain such a network, a mobile robot travels from node to node to recharge each sensor before its battery runs out. Consider each node's recharge as a real-time task, the robot needs to serve these tasks by their deadlines. This represents a class of challenging mobility scheduling problems, where the nodes' deadlines and spatial distribution are often at odds with each other. In this paper, we focus on the scenario where nodes have heterogeneous energy consumption rates, and our goal is to maximize the percentage of nodes alive. We formulate this scheduling problem and prove its NP-completeness. To solve this problem, we propose a spatial dependent task scheduling algorithm, which quantifies the impact of scheduling proximate tasks on the other tasks. With extensive simulations, we reveal the trade-offs of existing solutions under a wide range of network scenarios. Our evaluation results show that our algorithms out-perform classical TSP scheduler by up to 10% and 85% in terms of coverage ratio and average tardiness, respectively.